VOLUME 126 MONTHLY WEATHER REVIEW DECEMBER 1998 Tropical Cyclone Eye Thermodynamics H. E. WILLOUGHBY Hurricane Research Division, AOML/NOAA, Miami, Florida (Manuscript received 10 June 1997, in ®nal form 17 February 1998) ABSTRACT In intense tropical cyclones, sea level pressures at the center are 50±100 hPa lower than outside the vortex, but only 10±30 hPa of the total pressure fall occurs inside the eye between the eyewall and the center. Warming by dry subsidence accounts for this fraction of the total hydrostatic pressure fall. Convection in the eyewall causes the warming by doing work on the eye to force the thermally indirect subsidence. Soundings inside hurricane eyes show warm and dry air aloft, separated by an inversion from cloudy air below. Dewpoint depressions at the inversion level, typically 850±500 hPa, are 10±30 K rather than the ;100 K that would occur if the air descended from tropopause level without dilution by the surrounding cloud. The observed temperature and dewpoint distribution above the inversion can, however, be derived by ;100 hPa of undilute dry subsidence from an initial sounding that is somewhat more stable than a moist adiabat. It is hypothesized that the air above the inversion has remained in the eye since it was enclosed when the eyewall formed and that it has subsided at most a few kilometers. The cause of the subsidence is the enclosed air's being drawn downward toward the inversion level as the air below it ¯ows outward into the eyewall. Shrinkage of the eye's volume is more than adequate to supply the volume lost as dry air is incorporated into the eyewall or converted to moist air by turbulent mixing across the eye boundary. The moist air below the inversion is in thermodynamic contact with the sea surface. Its moisture derives from evaporation of seawater inside the eye, frictional in¯ow of moist air under the eyewall, and from moist downdrafts induced as condensate mixes into the eye. The moist air's residence time in the eye is much shorter than that of the dry air above the inversion. The height of the inversion is determined by the balance between evaporation, in¯ow, and inward mixing on one hand and loss to the eyewall updrafts on the other. 1. Introduction tensi®es. Because the subsiding air is warmer than any other air in the cyclone, the descent must consume en- The lowest surface pressure in a hurricane coincides ergy released elsewhere in the storm. with the axis of vortex rotation inside the eye. The swirl- Balanced models predict, and observations con®rm, ing windÐthe tangential component of the wind vector that the most rapid pressure falls are con®ned to the in storm-centered cylindrical coordinatesÐincreases area inside the eyewall wind maximum (Shapiro and with distance outward from the axial stagnation point Willoughby 1982; Schubert and Hack 1982; Willoughby to the radius of maximum wind at the inner edge of the et al. 1982; Willoughby 1990). Tightening of the pres- eyewall. The eyewall, a ring of cumulonimbus convec- sure gradient across the wind maximum causes the wind tion, surrounds the eye and contains the sharpest radial to increase at, and inward from, the radius of maximum pressure gradient nearly coincident with strongest wind. wind so that the eyewall contracts as the wind strength- Because the eyewall slopes outward, the eye is approx- ens. Dynamically or thermodynamically forced out¯ow imately an inverted, truncated cone. The air aloft in the from the lower part of the eye into the eyewall causes eye is clear, warm, and dry, separated by an inversion the sinking and adiabatic warming, and hence the pres- from more moist, usually cloudy air near the surface sure falls. Inside the eye, where the wind increases with (Jordan 1952). Subsidence is the source of the eye's radius, air must subside from above to replace the loss warmth and dryness. Subsidence-induced adiabatic to the eyewall because horizontal motion is constrained warming increases the thickness between the ®xed tro- by the strong radial gradient of angular momentum. On popause height and the surface, lowering the hydrostatic the other hand, outside the eyewall, where the wind surface pressure at the vortex center as the cyclone in- decreases with radius and the radial angular momentum gradient is weaker, air can converge horizontally above the friction layer to replace the mass carried aloft by convection. This midlevel in¯ow from large radius sup- Corresponding author address: Dr. H. E. Willoughby, Hurricane Research Division AOML/NOAA, 4301 Rickenbacker Causeway, plies the angular momentum necessary to increase the Miami, FL 33143. swirling wind, in contrast with the frictional in¯ow near E-mail: [email protected] the surface, which extracts moist enthalpy from the sea 3053 3054 MONTHLY WEATHER REVIEW VOLUME 126 surface and feeds it into the convection, but can supply en subsidence. A conceptual model based upon this in- little excess angular momentum (Ooyama 1969, 1982). terpretation can synthesize observed eye soundings and The pressure fall between the eyewall and the center calculate realistic hydrostatic pressure falls from the accounts for only part of the total difference between eyewall inward to the axis of vortex rotation. the undisturbed surface pressure outside the storm and minimum sea level pressure (MSLP) at the center. The 2. Observed eye soundings process of bringing the late-summer tropical tropo- sphere into thermodynamic equilibrium with the sea sur- Eastern Paci®c Hurricane Olivia formed from a dis- face at 288±308C, taking into account the elevation of turbance on the ITCZ on 19 September 1994. It reached equivalent potential temperature as the pressure de- hurricane intensity early on 24 September, less than two clines, can produce hydrostatic pressures as low as the days after it had become a tropical storm (Pasch and minimum sea level pressures of the most intense tropical May®eld 1996). Late on the 24th at 1922 UTC, the cyclones. Thermodynamic arguments (e.g., Miller 1958; National Oceanic and Atmospheric Administration's Emanuel 1986) that relate maximum possible intensity WP-3D research aircraft began two days of operations of hurricanes to sea surface temperature (SST) are es- in the hurricane, providing clear documentation of the sentially elaborations of this result. Nevertheless, the in¯uences of environmental wind shear and SST on in- moist adjustment process is only part of the story be- tensity and structure. When the aircraft arrived in Olivia, cause the tropospheric column in real tropical cyclones the MSLP had fallen to 949 hPa as the storm moved in is generally undersaturated except in organized con- weak easterly environmental wind shear over warm wa- vection, such as the eyewall, in the stratocumulus deck ter with SST .288C. Olivia continued to intensify that caps the surface boundary layer, or in the out¯ow throughout the 4 h that the airplanes remained in the anvil near the tropopause. An airplane ¯ying outside of storm on the ®rst day. Subsequently, the MSLP appeared convection in the midtroposphere typically encounters to reach a minimum overnight at about 1200 UTC on precipitation, but little cloud. The eye itself is often the 25th. When the aircraft returned at 2021 UTC on clear, apart from boundary layer stratocumulus. This the 25th, Olivia's MSLP was 924 hPa, lower than on observation applies most consistently to intense tropical the previous day, but the storm ®lled throughout the rest cyclones that are continuing to intensify. Once inten- of the ¯ight in response to cooler SST and somewhat si®cation stops, but before the pressure has risen ap- stronger, then southwesterly, shear caused by an upper preciably, the eye typically ®lls with cloud (Jordan low northeast of the hurricane. By the time the aircraft 1961). left the storm on the second day, the MSLP had risen The conventional view of the eye's thermodynamics to 935 hPa. is that air detrains from the top of the eyewall and sinks A dropsonde observation in Olivia's eye at 2123 UTC inside the eye to the lower troposphere where it is en- on the 24th (Fig. 1a) is typical of intensifying tropical trained back into the eyewall. Inward mixing from the cyclones. It shows the expected inversion between 890 eyewall is hypothesized to force the subsidence and and 850 hPa, separating warm and dry air above from maintain the moisture and momentum budgets of the moist air below. In the moist air, the sounding follows subsiding air (Miller 1958; Malkus 1958; Holland a saturated adiabat down to 920 hPa and then a dry 1997). In this interpretation, the recirculation is rapid adiabat to the surface. Above the inversion, the dew- enough to replenish the eye's volume many times over point depression increases from 10 K at the top of the the hurricane's lifetime. The original argument for rapid inversion to 12 K at 600 hPa, the top of the sounding. replenishment of the air in the eye was that the calm The temperature and dewpoint soundings both run gen- air inside the eye did not appear to share in the trans- erally parallel to moist adiabats in the dry air, but with lation of the vortex as a whole (Malkus 1958), and that 1±3 K perturbations. Equivalent potential temperature, the eye moved by continuously reforming. More recent ue, has a weak minimum value of 350 K near 700 hPa observations from aircraft equipped with inertia navi- (Fig. 1b). It increases abruptly from 355 K at the top gation equipment show clearly that the low-level wind of the inversion layer to nearly 365 K at the bottom. is a superposition of circulation about the axis of ro- The vapor mixing ratio decreases from 11 gm kg21 just tation and the translation of the axis (Willoughby and above the inversion to about 7 gm kg21 at 600 hPa.